| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Limiting equilibrium both directions |
| Difficulty | Standard +0.3 This is a standard two-equation limiting equilibrium problem requiring resolution of forces parallel to the slope in both directions, then solving simultaneous equations. While it involves multiple steps and careful sign management, it follows a well-established method taught in M1 with no novel insight required—slightly easier than average due to its routine nature. |
| Spec | 3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
4 A block of mass 11 kg is at rest on a rough plane inclined at $30 ^ { \circ }$ to the horizontal. A force acts on the block in a direction up the plane parallel to a line of greatest slope. When the magnitude of the force is $2 X \mathrm {~N}$ the block is on the point of sliding down the plane, and when the magnitude of the force is $9 X \mathrm {~N}$ the block is on the point of sliding up the plane. Find\\
(i) the value of $X$,\\
(ii) the coefficient of friction between the block and the plane.
\hfill \mbox{\textit{CAIE M1 2011 Q4 [7]}}